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Representations of polynomial covariance type commutation relations by piecewise function multiplication and composition operators
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
Makerere University, Department of Mathematics, College of Natural Sciences, Kampala, Uganda.ORCID iD: 0000-0001-9658-1222
2023 (English)In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer, 2023, p. 233-257Conference paper, Published paper (Refereed)
Abstract [en]

Representations of polynomial covariance type commutation relations are constructed on Banach spaces Lp and C[α, β], α, β∈ R. Representations involve operators with piecewise functions, multiplication operators and inner superposition operators.

Place, publisher, year, edition, pages
Springer, 2023. p. 233-257
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 426
Keywords [en]
piecewise function, multiplication operators, covariance commutation relations
National Category
Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-62301DOI: 10.1007/978-3-031-32009-5_10Scopus ID: 2-s2.0-85162175330ISBN: 978-3-031-32008-8 (print)ISBN: 978-3-031-32009-5 (electronic)OAI: oai:DiVA.org:mdh-62301DiVA, id: diva2:1751893
Conference
International Conference on Stochastic Processes and Algebraic Structures — From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Funder
Sida - Swedish International Development Cooperation AgencyAvailable from: 2023-04-19 Created: 2023-04-19 Last updated: 2024-08-21Bibliographically approved
In thesis
1. Construction of Representations of Commutation Relations by Linear Operators in Banach Spaces
Open this publication in new window or tab >>Construction of Representations of Commutation Relations by Linear Operators in Banach Spaces
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is devoted to the construction and investigation of some properties of pairs of linear operators (A, B) (representations) satisfying commutation relations AB=BF(A), where F denotes certain polynomial. Commutation relations of this kind are called "covariance type" and finding their representations is equivalent to solving operator equations. This kind of commutation relations and operator representations on finite-dimensional or infinite-dimensional linear spaces are important in Physics, Engineering and many areas of Mathematics. The most original part of the present thesis contains the construction of representations of commutation relations AB=BF(A) by linear integral operators, multiplication operators and weighted composition operators defined on Banach spaces of continuous functions, on Lp spaces and lp spaces. Conditions on kernels of integral operators and functions defining multiplication and composition operators are derived for these operators to satisfy the covariance type commutation relations, both for the general polynomials F and for important specific choices of F. These conditions are used for construction of various concrete pairs of operators satisfying such commutation relations. Many essential algebraic properties of commutation relations are studied here as well.

Place, publisher, year, edition, pages
Västerås: Mälardalens universitet, 2023
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 382
National Category
Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-62303 (URN)978-91-7485-594-4 (ISBN)
Public defence
2023-05-29, Kappa, Mälardalens universitet, Västerås, 13:15 (English)
Opponent
Supervisors
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2023-04-20 Created: 2023-04-19 Last updated: 2023-05-08Bibliographically approved

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Citation style
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